Description
In this talk I will present some of our attempts to develop a mathematically rigorous theory of non-Markovian open quantum systems with Gaussian environments. I will show that, for a broad class of environments which strictly generalize the Markovian environment, a system-environment unitary group can be rigorously defined and, in many cases, can also be shown to be strongly-continuous two-parameter group. I will then go onto consider many-body lattice models with non-Markovian environment and establish a Lieb-Robinson bounds for these models. Finally, I will describe our recent work on developing quantum algorithms for simulating the dynamics of these models with near-optimal scaling on the system size and evolution time.
